1.1 Exploratory Analysis

Plot showing the growth of Upi Transaction volume and Transaction amount overtime(2016-2024)

Plot after log transform

The simultaneous growth of both factors is evident, and as anticipated, the growth of UPI transaction volume and transaction amount is nearly identical, despite the significant difference in their values. This is due to each transaction resulting in some amount of money being transferred, ranging from very small to very high values. Observing the presence of trends and seasonal components is difficult in this combined plot, so value and volume are plotted separately for clearer analysis.

Value and Volume of transactions per month

Plot of Average Transaction value

Average transaction value post September 2018

Number of Banks live in UPI

Number banks allowing UPI registration is growing rapidly this indicates at the growth of financial inclusion among the population of India the more banks especially regional banks allow UPI registrations the better will be the penetration of digitization of payments throughout the country.

1.2 Time Series Analysis of Monthly UPI Metrics.

Initially some classical methods such as smoothing procedures like Moving Average or filters are performed to dampen the fluctuations and then proceed to decompose the time series into several components.After this stochastic models maybe used, such as AR(Auto Regressive), MA(Moving Average) and if needed ARMA(Auto Regressive Moving Average Process) AND ARIMA(Auto Regressive Integrated Moving Average Process) to model the data, given the conditions to assume these models HOLD such as stationarity etc.

1.2.1 Analysing Time series with Trend and no Seasonal Variation(Monthly UPI Value & Volume of transaction)

From the exploratory analysis it was found that that monthly value and volume of UPI transactions contained a significant amount of secular positive trend with some underlying random component,there is no visible seasonal fluctuation in these data.

Trend- From (Kendall and Stuart 1966) “The concept of trend is more difficult to define. Generally, one thinks of it as a smooth broad motion of the system over a long term of years, but” long” in this connexion is a relative term, and what is long for one purpose may be short for another.”
The simplest type of trend is the familiar ‘linear trend + noise’, for which the observation at time t is a random variable \(X_t\), given by \[X_t = \alpha + \beta_t + \varepsilon_t .....(1)\] where \(\alpha\), \(\beta\) are constants and \(\epsilon_t\) denotes a random error term with zero mean. The mean level at time t is given by \[m_t = (\alpha + \beta_t) .....(2)\] this is sometimes called ‘the trend term’. Other writers prefer to describe the slope \(\beta\) as the trend, so that trend is the change in the mean level per unit time.The trend in Equation (1) is a deterministic function of time and is sometimes called a global linear trend. In practice, this generally provides an unrealistic model, and nowadays there is more emphasis on models that allow for local linear trends.This could be done deterministically, but it is more common to assume that \(\alpha\) and \(\beta\) evolve stochastically giving rise to what is called a stochastic trend.So far the models considered have been linear,another possibility, depending on how the data look, is that the trend has a nonlinear form, such as quadratic growth.(Chatfield 2016)

• Filtering- One of the most used procedure for dealing with a trend is to use a linear filter, which converts one time series, \({x_t}\)into another \({y_t}\), by the linear operation

  \[ y_t= \sum_{r=-q}^{+s}a_rx_{t+r} \] where \({a_r}\) is a set of weights. In order to smooth out local fluctuations and estimate the local mean, one should clearly choose the weights so that \(\sum{a_r}=1\), and then the operation is known as Moving Average. (Chatfield 2016)

There are many different choices for the weights of the moving average such as Spencer’s 15 Point Moving average weights , Henderson’s Moving average weights etc. Here the data is relatively small, so undertaking the end effects, the simple moving average with a 6 month order to smooth the data is used. This can be easily done using the ma() function in stats package .

Moving Average Trend

Both the plots are identical and it can be observed that the moving average has successfully removed most of the random fluctuations within the series .Considering the deterministic model to be \(Y_t=T_t+e_t\) where \(Y_t\),\(T_t\) and \(e_t\) represents the original series ,Trend component and the random component respectively then the moving Average values can be considered to be a good representative of the trend component.

Thus the calculated trend values are-

Month	Smoothed Value	Smoothed Volume
2016-04-01	NA	NA
2016-05-01	NA	NA
2016-06-01	NA	NA
2016-07-01	1.006583e+01	5.333333e-03
2016-08-01	2.248500e+01	8.583333e-03
2016-09-01	8.985083e+01	2.758333e-02
2016-10-01	2.901650e+02	8.058333e-02
2016-11-01	5.927033e+02	1.527500e-01
2016-12-01	9.532967e+02	2.408333e-01
2017-01-01	1.337894e+03	3.523333e-01
2017-02-01	1.747834e+03	4.870833e-01
2017-03-01	2.171754e+03	6.323333e-01
2017-04-01	2.513884e+03	7.617500e-01
2017-05-01	2.841721e+03	9.250000e-01
2017-06-01	3.268352e+03	1.233583e+00
2017-07-01	3.908953e+03	2.020000e+00
2017-08-01	4.880520e+03	3.398500e+00
2017-09-01	6.292865e+03	5.323083e+00
2017-10-01	8.145842e+03	7.618833e+00
2017-11-01	1.040663e+04	1.007550e+01
2017-12-01	1.322466e+04	1.258942e+01
2018-01-01	1.645890e+04	1.475767e+01
2018-02-01	2.009083e+04	1.640417e+01
2018-03-01	2.436408e+04	1.794742e+01
2018-04-01	2.969173e+04	1.980283e+01
2018-05-01	3.563823e+04	2.199067e+01
2018-06-01	4.153396e+04	2.506100e+01
2018-07-01	4.850223e+04	2.939517e+01
2018-08-01	5.657724e+04	3.462633e+01
2018-09-01	6.580261e+04	4.053683e+01
2018-10-01	7.579012e+04	4.697683e+01
2018-11-01	8.500796e+04	5.331992e+01
2018-12-01	9.552048e+04	5.961858e+01
2019-01-01	1.072439e+05	6.539442e+01
2019-02-01	1.186834e+05	6.962800e+01
2019-03-01	1.281991e+05	7.248608e+01
2019-04-01	1.349012e+05	7.485200e+01
2019-05-01	1.419197e+05	7.813283e+01
2019-06-01	1.482334e+05	8.146317e+01
2019-07-01	1.546768e+05	8.581358e+01
2019-08-01	1.618523e+05	9.291192e+01
2019-09-01	1.695801e+05	1.015710e+02
2019-10-01	1.800643e+05	1.102092e+02
2019-11-01	1.915534e+05	1.176265e+02
2019-12-01	2.009715e+05	1.234528e+02
2020-01-01	2.013704e+05	1.246447e+02
2020-02-01	2.004490e+05	1.235359e+02
2020-03-01	2.078221e+05	1.239047e+02
2020-04-01	2.189562e+05	1.257453e+02
2020-05-01	2.314633e+05	1.297910e+02
2020-06-01	2.479930e+05	1.368447e+02
2020-07-01	2.777872e+05	1.503892e+02
2020-08-01	3.117517e+05	1.674541e+02
2020-09-01	3.389974e+05	1.830621e+02
2020-10-01	3.635795e+05	1.972504e+02
2020-11-01	3.858628e+05	2.095791e+02
2020-12-01	4.110806e+05	2.229592e+02
2021-01-01	4.346986e+05	2.354673e+02
2021-02-01	4.519650e+05	2.429572e+02
2021-03-01	4.712014e+05	2.504796e+02
2021-04-01	4.967260e+05	2.631332e+02
2021-05-01	5.291555e+05	2.815311e+02
2021-06-01	5.594488e+05	2.997417e+02
2021-07-01	5.950527e+05	3.205767e+02
2021-08-01	6.413509e+05	3.474476e+02
2021-09-01	6.877903e+05	3.758284e+02
2021-10-01	7.298892e+05	4.018961e+02
2021-11-01	7.643424e+05	4.214067e+02
2021-12-01	8.055054e+05	4.441007e+02
2022-01-01	8.486793e+05	4.700653e+02
2022-02-01	8.890911e+05	4.961747e+02
2022-03-01	9.274760e+05	5.217177e+02
2022-04-01	9.623538e+05	5.464486e+02
2022-05-01	1.002099e+06	5.774768e+02
2022-06-01	1.035583e+06	6.060376e+02
2022-07-01	1.067595e+06	6.318502e+02
2022-08-01	1.099041e+06	6.574887e+02
2022-09-01	1.133770e+06	6.851637e+02
2022-10-01	1.175720e+06	7.161239e+02
2022-11-01	1.208953e+06	7.386541e+02
2022-12-01	1.247041e+06	7.624843e+02
2023-01-01	1.287827e+06	7.916278e+02
2023-02-01	1.328991e+06	8.224483e+02
2023-03-01	1.369988e+06	8.525426e+02
2023-04-01	1.405682e+06	8.811533e+02
2023-05-01	1.453650e+06	9.226448e+02
2023-06-01	1.496098e+06	9.636586e+02
2023-07-01	1.535885e+06	1.000167e+03
2023-08-01	1.582498e+06	1.036257e+03
2023-09-01	1.632338e+06	1.073801e+03
2023-10-01	1.686915e+06	1.114831e+03
2023-11-01	1.733480e+06	1.146123e+03
2023-12-01	NA	NA
2024-01-01	NA	NA
2024-02-01	NA	NA

The downside of this method is that it can not be used to make future prediction and also there’s an effect of missing end values due to moving average. It can be seen that the estimated trend values are very close the original values which falls with our initial assumption that this time series is made up of trend and random error only.

• Curve Fitting- While fitting a deterministic function of time as a curve the intital goal is to figure out what kind of a function might properly represent our time series. Everett Rogers in his book Diffusion of Innovations(2003) mentions “The logistic function can be used to illustrate the progress of the diffusion of an innovation through its life cycle” ,historically, when new products are introduced there is an intense amount of research and development which leads to dramatic improvements in quality and reductions in cost. This leads to a period of rapid industry growth. Some of the more famous examples are: railroads, incandescent light bulbs, electrification, cars and air travel. Eventually, dramatic improvement and cost reduction opportunities are exhausted, the product or process are in widespread use with few remaining potential new customers, and markets become saturated. UPI is a modern innovation which has revolutionized the way payments are done it may be a good idea to fit a logistic growth curve to the monthly value and volume data for UPI transactions.
  The Logistic Function in terms of time is given as- \[ y_t=\frac{k}{1+\exp(\frac{b-t}{a})} \] where \(y_t\) is the value of the time series at time t and a , b , k are constants.

There are many different methods to fit a logistic curve to our data most of these include long calculations for ease of calculations the SSlogis() function from stats package along with the nls() function in R may be used, SSlogis() employs a self starting logistic function using the input data(Period of time) and calculates constants k( Asymptote ), b( point of inflexion ) and a ( Scaling constant) , while nls() uses the model given by SSlogis to fit the data using non linear least squares.

Plotting the Calculated model-

Fitting logistic curve to Monthly UPI value metric

From the fitted model it can be seen that the model choice was decent as the data seems to be very close to the fitted line. Here The estimated values for the constants are given -

Estimates for Logistic Fit

term	estimate	std.error	statistic	p.value
k	2.436074e+06	6.826906e+04	35.68342	0
b	7.974670e+01	8.953216e-01	89.07046	0
a	1.408733e+01	3.238176e-01	43.50392	0

from this the calculated equation becomes -

\[ y_t=\frac{2.436074e+06}{1+\exp(\frac{7.974670e+01 - t}{1.408733e+01})} \]

based on the equation the fitted values are

Logistic Curve fit for UPI Monthly Transaction Value

Time	Original Value	Fitted Value
2016-04-01	0.00	9065.907
2016-05-01	0.00	9730.185
2016-06-01	0.00	10442.926
2016-07-01	0.38	11207.636
2016-08-01	3.09	12028.065
2016-09-01	32.64	12908.232
2016-10-01	48.57	13852.438
2016-11-01	100.46	14865.287
2016-12-01	707.93	15951.705
2017-01-01	1696.22	17116.961
2017-02-01	1937.71	18366.692
2017-03-01	2425.14	19706.925
2017-04-01	2271.24	21144.100
2017-05-01	2797.07	22685.100
2017-06-01	3098.36	24337.278
2017-07-01	3411.35	26108.484
2017-08-01	4156.62	28007.097
2017-09-01	5325.81	30042.056
2017-10-01	7057.78	32222.894
2017-11-01	9669.33	34559.772
2017-12-01	13174.24	37063.512
2018-01-01	15571.20	39745.638
2018-02-01	19126.20	42618.409
2018-03-01	24172.60	45694.862
2018-04-01	27021.85	48988.846
2018-05-01	33288.51	52515.066
2018-06-01	40834.03	56289.117
2018-07-01	51843.14	60327.531
2018-08-01	54212.26	64647.806
2018-09-01	59835.36	69268.451
2018-10-01	74978.27	74209.018
2018-11-01	82232.21	79490.135
2018-12-01	102594.82	85133.538
2019-01-01	109932.43	91162.096
2019-02-01	106737.12	97599.832
2019-03-01	133460.72	104471.936
2019-04-01	142034.39	111804.777
2019-05-01	152449.29	119625.901
2019-06-01	146566.35	127964.018
2019-07-01	146386.64	136848.980
2019-08-01	154504.89	146311.748
2019-09-01	161456.56	156384.338
2019-10-01	191359.94	167099.754
2019-11-01	189229.09	178491.902
2019-12-01	202520.76	190595.477
2020-01-01	216242.97	203445.834
2020-02-01	222516.95	217078.833
2020-03-01	206462.31	231530.647
2020-04-01	151140.66	246837.552
2020-05-01	218391.60	263035.680
2020-06-01	261835.00	280160.743
2020-07-01	290537.86	298247.717
2020-08-01	298307.61	317330.502
2020-09-01	329027.66	337441.537
2020-10-01	386106.74	358611.397
2020-11-01	390999.15	380868.344
2020-12-01	416176.21	404237.864
2021-01-01	431181.89	428742.169
2021-02-01	425062.76	454399.691
2021-03-01	504886.44	481224.557
2021-04-01	493663.68	509226.066
2021-05-01	490638.65	538408.169
2021-06-01	547373.17	568768.964
2021-07-01	606281.14	600300.220
2021-08-01	639116.95	632986.945
2021-09-01	654351.81	666807.003
2021-10-01	771444.98	701730.797
2021-11-01	768436.11	737721.034
2021-12-01	826848.22	774732.583
2022-01-01	831993.11	812712.437
2022-02-01	826843.00	851599.782
2022-03-01	960581.66	891326.194
2022-04-01	983302.27	931815.955
2022-05-01	1041520.00	972986.503
2022-06-01	1014384.00	1014748.995
2022-07-01	1062991.00	1057009.002
2022-08-01	1072792.68	1099667.300
2022-09-01	1116438.10	1142620.768
2022-10-01	1211582.51	1185763.359
2022-11-01	1190593.39	1228987.138
2022-12-01	1282055.01	1272183.353
2023-01-01	1298726.62	1315243.531
2023-02-01	1235846.62	1358060.559
2023-03-01	1410443.01	1400529.748
2023-04-01	1407007.55	1442549.834
2023-05-01	1489145.44	1484023.915
2023-06-01	1475464.27	1524860.300
2023-07-01	1533645.20	1564973.249
2023-08-01	1576536.56	1604283.603
2023-09-01	1579133.18	1642719.293
2023-10-01	1715768.34	1680215.717
2023-11-01	1739740.61	1716716.001
2023-12-01	1822949.42	1752171.123
2024-01-01	1841083.97	1786539.937
2024-02-01	1827869.33	1819789.073

Based on this curve fitting the future estimates for the next 12 months will be

Prediction for Monthly Values

Month	Predicted Value
2024-03-01	1851893
2024-04-01	1882832
2024-05-01	1912597
2024-06-01	1941181
2024-07-01	1968585
2024-08-01	1994817
2024-09-01	2019888
2024-10-01	2043815
2024-11-01	2066618
2024-12-01	2088321
2025-01-01	2108951
2025-02-01	2128537

Applying the same steps for transaction volume gives us -

Logistic curve fit to Monthly UPI volume metric

Estimates from Logistic -Curve Fit for Volume

term	estimate	std.error	statistic	p.value
k	2006.45018	81.6561476	24.57194	0
b	88.00355	1.2140952	72.48488	0
a	14.83489	0.3258464	45.52724	0

from this the calculated equation becomes -

\[ y_t=\frac{2006.45018}{1+\exp(\frac{ 88.00355 - t}{14.83489})} \]

based on the equation the fitted values are

Logistic Curve fit for UPI Monthly Transaction Volume

Time	Original Volume	Fitted Volume
2016-04-01	0.000	5.677418
2016-05-01	0.000	6.072121
2016-06-01	0.000	6.494175
2016-07-01	0.009	6.945462
2016-08-01	0.009	7.427994
2016-09-01	0.009	7.943916
2016-10-01	0.010	8.495520
2016-11-01	0.029	9.085252
2016-12-01	0.199	9.715722
2017-01-01	0.446	10.389716
2017-02-01	0.438	11.110205
2017-03-01	0.637	11.880361
2017-04-01	0.720	12.703563
2017-05-01	0.936	13.583418
2017-06-01	1.035	14.523768
2017-07-01	1.163	15.528709
2017-08-01	1.680	16.602605
2017-09-01	3.098	17.750104
2017-10-01	7.696	18.976158
2017-11-01	10.502	20.286035
2017-12-01	14.564	21.685343
2018-01-01	15.183	23.180048
2018-02-01	17.140	24.776491
2018-03-01	17.805	26.481416
2018-04-01	19.008	28.301985
2018-05-01	18.948	30.245804
2018-06-01	24.637	32.320946
2018-07-01	27.375	34.535974
2018-08-01	31.202	36.899965
2018-09-01	40.587	39.422537
2018-10-01	48.236	42.113871
2018-11-01	52.494	44.984737
2018-12-01	62.017	48.046520
2019-01-01	67.275	51.311246
2019-02-01	67.419	54.791601
2019-03-01	79.954	58.500959
2019-04-01	78.179	62.453402
2019-05-01	73.354	66.663741
2019-06-01	75.454	71.147536
2019-07-01	82.229	75.921106
2019-08-01	91.835	81.001549
2019-09-01	95.502	86.406745
2019-10-01	114.836	92.155365
2019-11-01	121.877	98.266865
2019-12-01	130.840	104.761483
2020-01-01	130.502	111.660224
2020-02-01	132.569	118.984836
2020-03-01	124.684	126.757779
2020-04-01	99.957	135.002187
2020-05-01	123.450	143.741812
2020-06-01	133.693	153.000958
2020-07-01	149.736	162.804403
2020-08-01	161.883	173.177307
2020-09-01	180.014	184.145099
2020-10-01	207.162	195.733347
2020-11-01	221.023	207.967620
2020-12-01	223.416	220.873315
2021-01-01	230.273	234.475475
2021-02-01	229.290	248.798585
2021-03-01	273.168	263.866345
2021-04-01	264.106	279.701425
2021-05-01	253.957	296.325199
2021-06-01	280.751	313.757464
2021-07-01	324.782	332.016138
2021-08-01	355.555	351.116945
2021-09-01	365.430	371.073098
2021-10-01	421.865	391.894956
2021-11-01	418.648	413.589699
2021-12-01	456.630	436.160993
2022-01-01	461.715	459.608666
2022-02-01	452.749	483.928401
2022-03-01	540.565	509.111448
2022-04-01	558.305	535.144370
2022-05-01	595.520	562.008822
2022-06-01	586.275	589.681375
2022-07-01	628.840	618.133395
2022-08-01	657.963	647.330975
2022-09-01	678.080	677.234942
2022-10-01	730.542	707.800923
2022-11-01	730.945	738.979491
2022-12-01	782.949	770.716385
2023-01-01	803.689	802.952808
2023-02-01	753.476	835.625798
2023-03-01	868.530	868.668673
2023-04-01	889.814	902.011534
2023-05-01	941.519	935.581838
2023-06-01	933.506	969.305012
2023-07-01	996.461	1003.105105
2023-08-01	1058.602	1036.905470
2023-09-01	1055.569	1070.629458
2023-10-01	1140.879	1104.201112
2023-11-01	1123.529	1137.545846
2023-12-01	1202.023	1170.591099
2024-01-01	1220.302	1203.266954
2024-02-01	1210.268	1235.506702

Based on this curve fitting the future estimates for the next 12 months will be-

Prediction for Monthly UPI Volume of Transaction

Month	Predicted Value
2024-03-01	1267.247
2024-04-01	1298.430
2024-05-01	1329.001
2024-06-01	1358.909
2024-07-01	1388.112
2024-08-01	1416.570
2024-09-01	1444.248
2024-10-01	1471.118
2024-11-01	1497.157
2024-12-01	1522.346
2025-01-01	1546.672
2025-02-01	1570.126

A long term prediction for both value and volume can be given via a plot as -

Long Term Forecast Via Logisitic Curve

Since the assumed model is non linear so \(R^2\) is not suitable as a model adequacy checker,to overcome this the residuals are checked via a normal qqplot

From the previous qqplot, The residuals are kind of linear with some significant tail values drifting outside the line this usually indicates a fat tail .Due to the extremely large values some deviations may have been too big, there is also a possibility of some outliers which could’ve caused this.

Foundings-

• It is found that by the year 2025 Volume of monthly transactions will cross 1500 crores and value of monthly transactions will cross 2000000 crores.
• It is expected that by the year 2027 both of these metrics will start to stabilize, although this is dependent on many other factors which have not been considered in the study these include availability of smartphones and fast internet connection for the percentage of population. But never the less this is an expectable figure.

1.3 Stochastic Analysis of monthly Per Transaction Value

Displaying Per Transaction and Differenced Time Series

Displaying Per Transaction and Differenced Time Series

The ACF cuts off at lag 1, and the PACF shows a significant value at lag 1. After differencing, there are no significant autocorrelation values in the time series. Assuming no seasonal effects, the differenced time series can be defined as a random walk model. \[ y_t=y_{t-1}+\varepsilon_t \] Which in ARIMA terms is written as ARIMA(0,1,0). Checking the auto.arima() output and see if the model selection aligns with the previous analysis is

## Series: . 
## ARIMA(0,1,0) 
## 
## sigma^2 = 9998:  log likelihood = -439.75
## AIC=881.51   AICc=881.56   BIC=883.8

It appears that the predicted forecast remains constant, specifically matching the last observation. This outcome arises because random walks permit only naive predictions, lacking discernible patterns. Additional forecasts, such as Simple Exponential Smoothing and Holt-Winters Exponential Smoothing, could be plotted for comparison.

Forecasts Based on SES and Holtwinters

As it can be seen SES gives a naive constant forecast which is the same as the ARIMA forecast. Holt-Winters on the other hand gives a rather interesting looking prediction, the predicted values are given as -

Here is the accuracy measure for this model.

1.4 Analyzing monthly growth rate for transaction volume.

The monthly growth rate relative to past month is calculated using this function-

#Calculating growth rate####
dat<-list()
#This Function Calculates the growth rate#
month_growth<-
  function(data,returndat)
  {
    returndat[1]=0;
    for(i in 2:length(data)){
      if(data[i-1]>0)
      {
        returndat[i]=(((data[i]-data[i-1])/data[i-1])*100)
      }
      else if(data[i-1]==0)
        returndat[i]=0
    }
    returndat
  }
growth<-matrix(month_growth(as.numeric(data1$`Volume(In Cr)`),dat),ncol=1)
growth<-data.frame(as.numeric(growth))
colnames(growth)<-c("GrowthRate")

Monthly Growth Rate

Monthly Growth Rate discarding intital volatility

Visually the data looks kind of stationary , to confirm this assumption Augmented Dickey Fueller Test is used to look for unit roots and find if the data is truly stationary or not and also find the lag order.Here the assumed significance level is 0.05.

## Warning in adf.test(growth1): p-value smaller than printed p-value

It can be observed that the p value for the test is less than the assumed significance level of 0.05 .So the null hypothesis is rejected and it can be concluded that the data is stationary.

ACF For Monthly growth rate

from the plot it is found that the process acf is identical to a white noise process.Some short term predictions for the monthly growth rate can be made using a Simple Exponential Smoothing forecast this is done using the ses() function in forecast package.

SES Forecast

Holt-Winters Forecast

From the accuracy measures we can see that the Holt-Winters Model turned out to be better than the SES model, based on accuracy measures like MAE,MASE etc.

2.1 Inlfation in India

Monthly Aggregated CPI

As it can be seen there is a steady increase of CPI in this period with some mild dips in some certain sections,this means there is a linear increase in inflation through the years.To overcome the effect of inflation in our Value of Transaction data we can use the index numbers for deflation, but even then the figures might not be a true representation of the actual situation because there might be even more such variables which have an underlying significant effect in value of transactions.

• This suggests it will be better to analyzye volume of transactions

Since-

1. This is independent of inflation since prices increasing doesn’t mean number of transactions have to increase,it doesn’t imply reduction in number of transactions also, since even though increasing prices may lead consumers to stop buying certain objects but th requirement for that object still needs to be fulfilled a transaction has to happen.

2. It was seen that the growth of both value and volume of payments have been nearly identical so forecasting one can give idea of future forecasts for the other.

3.1 Exploratory Data Analysis

The first few rows of the data set is –

It can be seen that in terms of Volume UPI leads the way and is much higher than other digital banking methods, Although in terms of Value(Not shown in the table but acessible fro the data source) Methods like RTGS and NEFT are far superior.

Plotting the daily UPI transaction volume

Daily UPI Transaction Volume

Zoomed Graph

From the plot, it’s evident that at the start of each month, the transaction volume reaches its peak, which then gradually decreases throughout the month until another peak is reached at the beginning of the following month. This pattern represents a monthly seasonal component. Additionally, this seasonal component appears to be increasing along with a trend in the data. Therefore, it would be appropriate to consider a multiplicative decomposition when decomposing the data.

3.2 Stochastic Modelling & Forecasting.

So far stochastic models have been rarely used to analyze our dataset, now moving to a more sophisticated analysis and forecast using Stochastic Models like AR ,MA,ARMA,ARIMA &SARIMA .To validate our models the data may be split into test and training parts to check for accuracy measures. The Auto Correlation function and the Partial Autocorrelation Function maybe plotted to see if the process can be identified.

3.2.1 ARIMA Modeling -

The General ARIMA(p,d,q) model is defined as \[ Wt = \alpha_1W_{t-1} +\dots + \alpha_pW_{t-p} + Z_t + \dots + \beta_qZ_{t-q} \] Where the process is a combination of \(AR(p)\) &\(MA(q)\) terms. One of the primary assumptions of stochastic modelling is stationarity, although ARIMA does not explicitly requires stationarity since it uses the d parameter as number of differences required to achieve stationarity, but even then the general ARIMA model is not suited for Seasonal data, infact the Extended Seasonal ARIMA model can only take seasonality for weeks or years but there aren’t really any such general models for monthly seasonality as it can seen already talked about in the Issues paragraph.If these are ignored then using the auto.arima function to fit an ARIMA model the results are -

## 
##  Fitting models using approximations to speed things up...
## 
##  ARIMA(2,1,2) with drift         : 17161.58
##  ARIMA(0,1,0) with drift         : 17410.9
##  ARIMA(1,1,0) with drift         : 17284.3
##  ARIMA(0,1,1) with drift         : 17242.15
##  ARIMA(0,1,0)                    : 17409.97
##  ARIMA(1,1,2) with drift         : 17159.98
##  ARIMA(0,1,2) with drift         : 17231.3
##  ARIMA(1,1,1) with drift         : 17191.76
##  ARIMA(1,1,3) with drift         : 17161.99
##  ARIMA(0,1,3) with drift         : 17227.03
##  ARIMA(2,1,1) with drift         : 17161.67
##  ARIMA(2,1,3) with drift         : 17161.96
##  ARIMA(1,1,2)                    : 17200
## 
##  Now re-fitting the best model(s) without approximations...
## 
##  ARIMA(1,1,2) with drift         : 17168.56
## 
##  Best model: ARIMA(1,1,2) with drift

## Series: UPI Volume of Daily Transactions 
## ARIMA(1,1,2) with drift 
## 
## Coefficients:
##          ar1      ma1     ma2   drift
##       0.7930  -1.2040  0.2273  2.8383
## s.e.  0.0267   0.0394  0.0369  0.2677
## 
## sigma^2 = 7953:  log likelihood = -8579.26
## AIC=17168.52   AICc=17168.56   BIC=17194.92
## 
## Training set error measures:
##                      ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -0.2706182 89.02712 59.52952 -0.653771 3.613357 0.9234873
##                       ACF1
## Training set -0.0004667928

Here the chosen model is ARIMA(1,1,2). \[ W_t=0.79W_{t-1}-1.2040Z_{t-1}+0.2273Z_{t-2} \] This is a non seasonal model², but our data definitely has some seasonal pattern within it , so the model chosen through auto.arima() doesn’t seem really ideal this time.
Looking at the forecasts for the next 30 days-

Forecast using ARIMA without considering seasonality

The forecast seems naive and shows no seasonal pattern.

Acuuracy Measures for ARIMA

	ME	RMSE	MAE	MPE	MAPE	MASE	ACF1
Training set	-0.2789604	72.3474	50.05477	-0.6376543	3.977516	0.8948011	0.0006335
Test set	320.7306098	412.2910	335.39521	7.7353686	8.212111	5.9956724	NA

The Accuracy measures may be noted for future comparison.

3.2.2 Using a Dynamic Regression Model

To find a way to incorporate the seasonality, a dynamic regression model with ARIMA errors where the explanatory variables are fourier terms (where each term is a sin cos pair) may be used, since fourier terms contain a wave pattern they could be useful to simulate the effect of seasonality, the dynamic regression model is given as - \[ y_t = \beta_0 + \beta_1 x_{1,t} + \dots + \beta_k x_{k,t} + \eta_t \] Except in this case \(\sum \beta_kx_{k,t}\) is replaced with\(\phi_t(k)\) where \(\phi_t(k)\) is a linear combination of \(k\) pairs of sin cos terms each having separate coefficients, This is also known as Dynamic Harmonic Regression.Here \(\eta_t\) is an ARIMA error term.

## Series: Daily UPI Value of Transaction 
## Regression with ARIMA(2,1,2) errors 
## 
## Coefficients:
##          ar1      ar2      ma1     ma2   drift     S1-30    C1-30    S2-30
##       0.7868  -0.0099  -1.2163  0.2416  2.8361  -43.8546  -6.0005  -0.4362
## s.e.  0.1597   0.1050   0.1574  0.1510  0.2672    8.5865   8.5642   5.9145
##         C2-30    S3-30   C3-30    S4-30    C4-30
##       -1.6658  -3.3898  1.9874  -4.2037  -3.0016
## s.e.   5.9083   4.4865  4.4854   3.6927   3.6933
## 
## sigma^2 = 7852:  log likelihood = -8565.42
## AIC=17158.84   AICc=17159.13   BIC=17232.77

Here 4 fourier terms have been added to the ARIMA model to simulate the seasonality ,it can be seen that the main ARIMA model is a (2,1,2) model i.e it has an AR order of 2 , MA order of 2 and the times the data has been differenced is equal to 1.There is a drift component as well, which is usually the case for data with trend.

Forecasts after adding fourier terms to the ARIMA model

From the plot it can be seen that adding fourier terms was a good idea since now the forecast does account for the monthly seasonality.But even then the problem persists since the period of months isn’t really equal and for that reason the result is a smoothed curve as forecast.The data is now split to check for accuracy measures.

Acuuracy Measures for Dynamic Harmonic Regression

	ME	RMSE	MAE	MPE	MAPE	MASE	ACF1
Training set	-0.3696803	73.24721	50.74154	-0.6451053	3.923337	0.8953204	-0.0002667
Test set	135.5477912	302.71755	243.15452	2.8056679	6.109612	4.2903940	NA

The accuracy measures show improvement from the previous model.
Here are the forecasted values-

Forecast of Daily UPI Volume of Transactions

	Point.Forecast	Lo.80	Hi.80	Lo.95	Hi.95
2024-05-24	4413.169	4299.611	4526.728	4239.497	4586.842
2024-05-25	4447.406	4316.666	4578.146	4247.456	4647.355
2024-05-26	4478.260	4337.291	4619.229	4262.666	4693.853
2024-05-27	4507.741	4360.151	4655.330	4282.022	4733.460
2024-05-28	4534.722	4382.629	4686.816	4302.116	4767.329
2024-05-29	4556.540	4401.251	4711.830	4319.045	4794.035
2024-05-30	4570.935	4413.287	4728.584	4329.833	4812.038
2024-05-31	4577.773	4418.318	4737.229	4333.907	4821.639
2024-06-01	4579.453	4418.563	4740.342	4333.393	4825.512
2024-06-02	4579.698	4417.631	4741.765	4331.837	4827.559
2024-06-03	4581.472	4418.407	4744.536	4332.086	4830.857
2024-06-04	4585.313	4421.381	4749.245	4334.601	4836.026
2024-06-05	4589.168	4424.462	4753.874	4337.273	4841.063
2024-06-06	4589.829	4424.419	4755.239	4336.856	4842.802
2024-06-07	4585.101	4419.037	4751.164	4331.129	4839.072
2024-06-08	4575.332	4408.654	4742.010	4320.421	4830.243
2024-06-09	4563.388	4396.126	4730.651	4307.583	4819.194
2024-06-10	4553.105	4385.280	4720.929	4296.439	4809.771
2024-06-11	4547.222	4378.852	4715.591	4289.723	4804.721
2024-06-12	4546.092	4377.192	4714.993	4287.781	4804.403
2024-06-13	4547.902	4378.481	4717.323	4288.794	4807.009
2024-06-14	4550.167	4380.235	4720.100	4290.278	4810.057
2024-06-15	4551.470	4381.032	4721.907	4290.808	4812.132
2024-06-16	4552.283	4381.346	4723.220	4290.857	4813.709
2024-06-17	4554.431	4382.999	4725.862	4292.248	4816.613
2024-06-18	4559.624	4387.702	4731.547	4296.691	4822.557
2024-06-19	4568.155	4395.745	4740.566	4304.477	4831.834
2024-06-20	4578.653	4405.758	4751.548	4314.233	4843.073
2024-06-21	4589.070	4415.693	4762.448	4323.912	4854.228
2024-06-22	4598.168	4424.311	4772.026	4332.276	4864.060

3.3 Forecast Based on Decomposition

Forecast Based on STL and Exponential Smoothing

Visually the forecast seems much better than the previous ones as it seems to incorporate the seasonal pattern much better.The Model is given by-

## ETS(A,A,N) 
## 
## Call:
##  ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend) 
## 
##   Smoothing parameters:
##     alpha = 0.2036 
##     beta  = 1e-04 
## 
##   Initial states:
##     l = 27.1008 
##     b = 0.0293 
## 
##   sigma:  0.6889
## 
##      AIC     AICc      BIC 
## 9502.829 9502.870 9529.236

Here the model is ETS(A,A,N) which is defined as Holt’s linear method with additive errors. This model consists of a measurement equation that describes the observed data, and some state equations that describe how the unobserved components or states (level, trend, seasonal) change over time. Hence, this is referred to as state space models. For this model, we assume that the one-step-ahead training errors are given by \(\varepsilon_t=y_t-\ell_{t-1}-b_{t-1} \sim NID(0,\sigma^2)\) Substituting this into the error correction equations for Holt’s linear method we obtain
\(y_t=\ell_{t-1}+b_{t-1}+\varepsilon_t,\)
\(\ell_t=\ell_{t-1}+b_{t-1}+\alpha \varepsilon_t,\)
\(b_t=b_{t-1}+\beta\varepsilon_t\)

where, for simplicity, we have set \(\beta=\alpha \beta^*\), here \(y_t\) is the forecast equation, and \(l_t\) and \(b_t\) are the two smoothing equations.

Accuracy measures MAPE,MASE ³ etc can be used, Hyndman in his book(Robin John Hyndman and Athanasopoulos 2018) suggests MASE is the best measure for accuracy for comparison between different models based on seasonal data.From the tables(??,??,??) MASE for the STL +ETS model is the lowest compared to the others,so it can be concluded that the model based on STL decomposition and Exponential Smoothing gives the best results.

4.1 EDA

Comparsion Between different Payment categories

It can be seen that except the less than 500 category of Peer to Peer and person to merchant payments the other categories have not shown any significant changes throughout this period,it may also be noted that while less than 500 Peer to Peer payments are decreasing person to merchant are increasing in a quite inverse proportion.Infact the correlation between the two is given as \(\rho\)= -0.9934348,which is nearly a perfect negative correlation.There is a slight change in greater than 2000 Peer to Peer and (500-2000) Peer to Peer payments as it can be seen, there is a downward trend for both of them.

Comparison between p2p and p2m overtime

From the plot it can be seen that over time P2M(Person to Merchant) payments have overtaken P2P(Peer to Peer) payments , this indicates the wide-scale acceptance of UPI by merchants throughout india. In a country where a substantial number of people and businessmen are skeptical about digital payments this is a remarkable achievement since this implies a growing trust towards UPI and a much wider acceptance.

6.1 Security Concerns-

What’s at stake?

• Virtual payment addresses
  
• Digital identity of individuals
  
• UPI ecosystem built and integrated for provisioning services
  
• Security of the identity, transaction information and data over the network
  
• Time to respond—transaction speed is the highest
  
• Customer confidence in the service, market trust and faster adoption by the customer
  
• Regulatory compliance
  
• Financial and reputational aspects

Whats being done?

According to the Reserve Bank’s Annual Report 2023–24, the number of frauds in the banking sector increased year-on-year to 36,075 out of which 29,082 digital/Card payment related.(Note that this only includes frauds of worth 1 lakh or above) . Specifically for the case of UPI there has been over 95000 frauds reported in the year 2023 This number is higher than the previous one since these include smaller frauds as well. Most of these frauds aren’t done through hacking or other technical means rather these are done via different scams and exploitative measures such as vishing⁵,fake UPI Id’s ,fake QR codes etc. to gain from innocent civillians and their trust in other human beings.

How to safeguard ?

The bedrock of UPI’s security architecture lies in its multi-factor authentication system. When you set up a UPI account, you link it to your mobile number, bank account, and a UPI Personal Identification Number (UPI-PIN). This multifactor authentication ensures that only the account HOLDer can initiate transactions, thus mitigating the risk of unauthorised access. Moreover, each transaction requires a UPI-PIN, acting as an additional layer of security.

• Digital literacy and educating individuals on the UPI payment methodology is indeed key in preventing users from falling prey to many of such frauds and the Indian government is regularly working on increasing awareness among the individuals.

• Besides this, many fintechs are also working to innovate newer Ways of Securing and Authenticating UPI payments in India. Some of the possible innovative ways in which UPI payments can be made more secure in India:

• Using biometric authentication for UPI payments such as multi-factor authentication for UPI payments could include biometric authentication, possibly through mobile devices, though the challenge at hand is that iris biometrics is not supported by a majority of smartphones in India.Adding on voice, finger, or face biometric authentication by validating the user’s voice/face with pre-saved audio/pic samples can be a breakthrough in enhancing the security of UPI payments in India.

6.2 Transaction Faults-

With a rise in number of transactions comes the obvious issue of load handling and digital capacity, there’s a limit to how many transactions the bank can process and not only the bank for a UPI payment there are multiple parties involved who need to be working simultaneously these include the concerned UPI app(G-Pay,PhonePe etc) senders bank and receivers bank also banks associated with creating the UPI Id etc.

Business Decline (BD) - Transaction decline due to a customer entering an invalid pin, incorrect beneficiary account etc. Or due to other business reasons such as exceeding per transaction limit, exceeding permitted count of transactions per day, exceeding amount limit for the day etc. Such declined transactions are termed as Business Decline. Any decline which is not because of a technical reason of the bank or NPCI is termed as business Decline.
Technical Decline (TD) - Transaction decline due to technical reasons, such as unavailability of systems and network issues on bank or NPCI side.
The main interest lies in how business declines and transaction declines have changed through the years and if the large number of upi transactions have resulted in more faults. To do this a weighted average is calculated where the weights are the ratio of total volume of transaction for a specific bank in a month and the total volume of transactions for all the banks for that month.The reason for such a choice of weight is, since some the banks such as SBI , Axis Bank etc. have very high user base while some have very low.

Transaction and Business decline overtime(Weighted averages)

It can be seen throughout the period that the transaction decline which is associated with upi servers and bank servers have been fairly low and is slowly decreasing which is an optimistic news since this means the technology handling these transactions are robust and it is suitable to assume that it will get even better with time.

Business Declines have always been higher than transaction decline but over time it can be seen that the numbers are decreasing showing increased literacy about UPI in the userbase further proving the wider acceptability of UPI.